The theoretical model of erosion processes in electrode spots during vacuum discharge during nanostructure formation is developed in the work. In this model the sources and drains of heat in electrode spots are considered in detail. Thus, the heat flux density generated by ions taking into account the emission cooling, reverse electric current and Nottingham heat is taken into account for the cathode, and both positive anode and negative potential declines are considered in describing the surface heat source for the anode. The distribution of current density in the element of the considered electrode volume was considered in sufficient detail for describing the volumetric heat source. Heat transfer from plasma radiation and convective heat transfer, and heat dissipation due to the shift of the plasma evaporation front and its radiation were considered for a more comprehensive description of the heat balance equation. The heat flux due to the movement of the stain was also taken into account. Thanks to the proposed model, the temperature fields near the spots and the rate of evaporation of the material during the life of the spot were determined, which allowed to determine the erosion coefficient for the electrode spot. According to the proposed model, calculations were performed for graphite electrodes. The dependence of the erosion coefficient on the lifetime of the spot and the current density at the electrodes is obtained. It is determined that at current density of more than 1011 A / м2 the probability of material emission in the form of clusters increases, which will prevent the appearance of nanostructures. Dependences of the erosion coefficient on the lifetime were obtained for both stationary and moving spots. The obtained dependences indicate the significant decrease in the erosion coefficient with increasing velocity of the spots. The determined theoretical values of current density coincide in order with the experimental values. The model can be used to determine the critical values of technological parameters in obtaining nanostructures for different electrode materials.